Many high speed rotating rotors, such as those on jet aircraft engines operate at speeds in excess of their resonant speeds, that is, above critical speed. Inasmuch as rotors for jet aircraft engines are required to be of light weight and are built up of numerous parts bolted together at thin flanges, they are relatively flexible. Furthermore, since the rotors carry the blading for the compressor turbine or fan sections, all of which are thin flexible members subject to erosion and edge fragmentation, the vibration of such rotors can become a serious problem.
Efforts to ameliorate this problem often consist of flexibly mounting the shaft bearings, which may be of roller and ball bearing types. Such mountings may be structurally elastic or the resiliency may be achieved by surrounding the outer bearing race by an oil cushion of small thickness, ranging from 2 to about 20 mil-inch. This oil cushion allows the bearing race to deflect, the oil offering flow resistance by virtue of its viscosity. This type of device acts as an energy absorber and therefore reduces the amplitude of vibration of the shaft.
Despite such means, many high speed engine rotors experience considerable trouble, including the rubbing of blade tips and possible bending and loss of blade tips due to large vibratory deflection. There have been repeated instances with some engines where the loss of part of a blade has so unbalanced the shaft that all the blades in a section of the engine were destroyed and, in some cases, the entire turbine rotor of the engine was torn loose and dropped from the airborne plane.
In 1930, a balancing machine for determining the unbalance in rotors of machines was invented by E. L. Thearle (reference may be made to Thearle, E. L.: A new type of dynamic Balancing Machine ASME, 1932, Paper APM-54-12). The machine had a spring-mounted bed 2 which supported a rotor 4 (FIG. 1) mounted in bearings 4A and 4B. The bed could be locked against motion in two spaced planes indicated by lines 6 and 8 by pivot pins in both sides of the bed at 2A or 2B. Determination of the degree of unbalance was accomplished by use of a balancing head 10, which was solidly coupled to the rotor and had two balls 12 and 14 (FIG. 3) mounted in a race 18 whose axis was colinear with that of the rotor 4. The balls were held from moving from their positions in the race by a spring loaded clutch not shown. The clutch could be removed from the balls by manually depressing the spring. A cycle of operation involves: (a) initial positioning of the balls 12 and 14 so that they are diametrically opposite each other and permitting motion of the bed in plane 8 by removing the pins at 2B; (b) rotating and increasing the speed of the rotor 4 to beyond the critical speed with head 10 in plane 8; (c) releasing the clutch and allowing the balls 12 and 14 to shift position; (d) restoring the clutch to lock the balls 12 and 14 in that position; (e) reducing speed and stopping rotation. When the rotor is brought to rest, inspection of the position of the balls 12 and 14 allows the magnitude and direction of the unbalance to be estimated, that is, the amount and location of correction weights in plane 8 can be determined. Replacing the pins at 2B, removing them at 2A and fastening the balancing head at plane 6 will allow the same procedure to be followed so that weight correction can be made at plane 6. Dynamic balancing of the rotor is thus completed.
The following discussion will clarify the operation of the balancing head 10. It is well known that in an unbalanced rotating shaft subjected to a centrifugal force rotating at shaft velocity below critical speed and with a low magnitude of damping, the displacement of the shaft due to the load is in phase with the load, that is, the direction of the load and the direction of the displacement which it causes rotate in the same radial plane. It is also well known that as the rotational velocity is increased to beyond critical, the phase angle between the direction of the force and the displacement becomes 180.degree.. Thus, above critical speed the displacement is opposite the heavy side of the shaft. With forced vibrations and with a single degree of freedom unbalance, the equation for the phase angle is given by ##EQU1## wherein: .phi. is the phase angle between the direction of the unbalanced force and the direction of the displacement;
C is the damping constant, that is, the proportionality factor, which, when multiplied by the rate of displacement, expresses the magnitude of a damping force acting opposite to the direction of the velocity of the displacement; PA1 C.sub.c is the critical damping constant, that is, the value of the damping constant which inhibits vibratory motion; PA1 W is the angular velocity of shaft rotation; PA1 W.sub.n is the angular velocity at the natural frequency of the shaft.
Calculated values of the displacement angle .phi., based on the above equation and using low values of damping are plotted on FIG. 6 to illustrate the shift in displacement angle as the shaft speed approaches and exceeds its natural frequency. Lines 20, 22 and 24 are plots of phase angle against (W/W.sub.n) using values of 0, 0.02 and 0.05 respectively for (C/C.sub.c).
In FIG. 4 the force and displacement conditions are illustrated for rotational velocities of the rotor 4 under the natural frequency. The point B represents the center axis of the bearing and S represents the center axis of the rotor 4. The distance between S and B is the displacement of the rotor under the action of the unbalanced load G. The centrifugal load G represented by an arrow and the displacement of S from B have the same direction. The system 12-S-14 and G orbit about B. The centrifugal forces on balls 12 and 14 are as indicated by the arrows 12A and 12B passing through them. If the balls are released, the tangential components of the centrifugal force drive the balls to the heavy side of the rotor as indicated by G, and increase the unbalance.
When the rotor speed exceeds the natural frequency, the displacement of S with respect to B is opposite to the direction of G as indicated in FIG. 5. Under these conditions, the centrifugal force on the balls 12 and 14 will urge them away from the direction of G and in the direction which will reduce the vibration. The weights cannot permanently overshoot the proper balancing condition, for if they should go beyond the proper location, the unbalance of the complete system, that is rotor plus weights will always shift the direction of the displacement so that it is opposite the direction of weight unbalance and the weights will shift to bring the system into balance.
Whereas balancing devices of the Thearle type have been used to test and correct the dynamic balance of rotors, they have not been used as permanent devices on rotors to immediately correct unbalance which might arise adventitiously during operation and thus avoid extensive damage due to vibration. The present invention is distinguished from Thearle by being a permanent device to automatically correct unbalance immediately as it may occur in rotors operating above critical speed. It is also distinguished in that the corrected balance is automatically maintained whenever the rotor speed is lowered to below critical speed. To accomplish this purpose, the balancing weights are held, fixed in position, whenever the rotor speed is below critical speed and the balancing weights are maintained completely free whenever the rotor speed is beyond some small increment above critical speed. This is accomplished automatically by a speed-dependent clutch device which may be actuated, for example, by mechanical, hydraulic or electrical means, none of which is taught by Thearle. In addition the invention involves novel weight structures not taught by Thearle.